Right, you'll never get a closed-form derivative for an explicit
function. Make it tacit:
(^.@-. % ]) deriv_jcalculus_ 1
(((_1 * %@-.) * ]) - ^.@-. * 1"0) % *:@]
The cases that are Lebesgue-integrable but not Riemann-integrable have
discontinuities or infinities that are inconsistent with digital
approximation, IIUC.
Henry Rich
On 1/15/2021 1:58 PM, Devon McCormick wrote:
The Lebesgue method is supposed to handle cases Riemann cannot.
I tried using the anti-derivatives from the calculus add-ons but cannot
make them work for an arbitrary user-defined function like "f3=: ] %~ [: ^.
-.".
On Fri, Jan 15, 2021 at 9:16 AM 'Pascal Jasmin' via Programming <
[email protected]> wrote:
The Riemann–Darboux approach seems so much easier. Just take a range and
a step interval (resolution) (all as y) to iterate the function (adverb
argument) and add all the results up divided by number of intervals times
range.
On Thursday, January 14, 2021, 04:21:19 p.m. EST, Devon McCormick <
[email protected]> wrote:
Has anyone looked into implementing a Lebesgue integration adverb in J?
This looks like a good explanation of it:
https://en.m.wikipedia.org/wiki/Lebesgue_integration .
--
Devon McCormick, CFA
Quantitative Consultant
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